Simultaneously Colouring the Edges and Faces of Plane Graphs

Journal article published in 1997 by Adrian O. Waller

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Publisher: Elsevier

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Abstract
In a simultaneous colouring of the edges and faces of a plane graph we colour edges and faces so that every two adjacent or incident pair of them receive different colours. In this paper we prove a conjecture of Mel'nikov which states that for this colouring every plane graph can be coloured withΔ+3 colours, whereΔis the maximum degree of a vertex in the graph.